Braid group actions on Kac–Moody Lie algebras and their integrable representations are classical. Lusztig initiated the study of braid group actions on quantized enveloping algebras associated with Kac–Moody Lie algebras. See [1]} for historical remarks. They are fundamental tools for the construction of the PBW bases of the quantized enveloping algebras of finite type in [2]}, [3]} (see also [4]}, [5]}, [6]}). Then Lusztig [7]} used the PBW basis for the construction of the canonical basis in ADE type. The braid group action is important also in affine type. Beck [8]} used it to construct the Drinfeld generators and proved the equivalence of two presentations of the quantized affine algebra.
